The property of a function of yielding out a derivative at a given point (x, f(x)).

The Requirement

  1. f(x) is continuous at x=c
  2. $\lim_{x→c^-} \frac {f(x)-f(c)} {x-c}=\lim_{x→c^+} \frac {f(x)-f(c)} {x-c}$

one side limits of the secant slope must equal

Not only continuous but must connect in a way that the slopes merge into each other smoothly

(So, that is why a absolute value function have its vertex a limit, but fails to be differentiable) In other words, the graph looks like a linear line if you zoom in (local linearity)

Types of Non Differentiable

  1. cusps
  2. vertical tangents
  3. sudden start or end
  4. sudden turn

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